90a3b6\sqrt{\ 90a^3b^6}

asked by guest
on Nov 14, 2024 at 11:54 pm



You asked:

Evaluate the expression: 90a3b6\sqrt{90 {a}^{3} {b}^{6}}

MathBot Answer:

Evaluated



90a3b6=310a3b6\displaystyle \sqrt{90 {a}^{3} {b}^{6}} = 3 \sqrt{10} \sqrt{a^{3} b^{6}}

Roots

90a3b6=i8100(re⁡(a3b6))2+8100(im⁡(a3b6))24sin⁡(atan2⁡(90im⁡(a3b6),90re⁡(a3b6))2)+8100(re⁡(a3b6))2+8100(im⁡(a3b6))24cos⁡(atan2⁡(90im⁡(a3b6),90re⁡(a3b6))2)≈9.48683298050514i((re⁡(a3b6))2+(im⁡(a3b6))2)0.25sin⁡(atan2⁡(90im⁡(a3b6),90re⁡(a3b6))2)+9.48683298050514((re⁡(a3b6))2+(im⁡(a3b6))2)0.25cos⁡(atan2⁡(90im⁡(a3b6),90re⁡(a3b6))2)\sqrt{90 {a}^{3} {b}^{6}} = i \sqrt[4]{8100 \left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + 8100 \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} + \sqrt[4]{8100 \left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + 8100 \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} \approx 9.48683298050514 i \left(\left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} + 9.48683298050514 \left(\left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)}90a3b6=i(−8100(re⁡(a3b6))2+8100(im⁡(a3b6))24sin⁡(atan2⁡(90im⁡(a3b6),90re⁡(a3b6))2))−8100(re⁡(a3b6))2+8100(im⁡(a3b6))24cos⁡(atan2⁡(90im⁡(a3b6),90re⁡(a3b6))2)≈−9.48683298050514i((re⁡(a3b6))2+(im⁡(a3b6))2)0.25sin⁡(atan2⁡(90im⁡(a3b6),90re⁡(a3b6))2)−9.48683298050514((re⁡(a3b6))2+(im⁡(a3b6))2)0.25cos⁡(atan2⁡(90im⁡(a3b6),90re⁡(a3b6))2)\sqrt{90 {a}^{3} {b}^{6}} = i \left(- \sqrt[4]{8100 \left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + 8100 \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)}\right) - \sqrt[4]{8100 \left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + 8100 \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} \approx - 9.48683298050514 i \left(\left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} - 9.48683298050514 \left(\left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)}

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